1946 年,物理学家 Stanislaw Ulam 在洛斯阿拉莫斯国家实验室研究核武器的项目中,提出了现代版本的马尔可夫链蒙特卡洛方法(Markov Chain Monte Carlo, MCMC),以代替传统的确定性数值算法。并且 Ulam 与同事 von Neumann,Metropolis 提议将这一绝密计划的代号命名为 Monte Carlo,这来源于他那经常借钱赌博的叔叔常去的...
Introduction to Markov chain Monte Carlo ( MCMC ) and its role in modern Bayesian analysisGregory, Phil
Corollary: If P has a limiting distribution π , then every row of Pt converges to π . TIME REVERSIBILITY Time reversibility drives almost any Markov Chain Monte Carlo algorithm. We will define the concept using the stationary distribution of the chain, which we shall show that is meaningful....
We also comment on how the convergence of a Markov chain to equilibrium can be assessed in practice and provide an illustrating example. Finally, we review some of the freely available, existing software for implementing MCMC methods. Keywords: Monte Carlo simulation; Markov chains; Bayesian ...
1. An Introduction to MCMC 15 Markov chain Monte Carlo (MCMC) algorithms are now widely used in virtually all areas of statistics. In particular, spatial applications featured very prominently in the early development of the methodology (Geman & Geman 1984), and they still provide some of the...
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov chain, Metropolis algorithm, continuous phase transition, statistical...
First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting...
Markov Chain Monte Carlo (HMCMC).Using Bayesian inference is the provably best method of combining data with domain knowledge to extract interpretable and insightful results that lead us towards better outcomes. In my opinion, this is what students need to learn to be clear-thinking and capable ...
基于这样一个Markov chain,就可以建模序列决策问题中状态流动的客观因素,而在MDP中,则可以通过引入reward和action来分别描述对于state的偏好以及agent做出的决策,从而建模序列决策问题中状态流动的主观因素。 1.2 Markov decision process 同样首先是介绍MDP的定义,如下图: MDP相对MC多的部分是引入的action,一个标准的MDP...
有几种方式能处理这个问题:MCMC(Markov Chain Monte Carlo)、Score Matching+Denoising Score Matching、NCE(Noise Contrastive Estimation),其中NCE广泛应用在自监督学习和VLM中 前两种方法此处有时间我再学习后展开介绍,当前主要介绍最后一种方法NCE: 相比从model distribution中采样negative sample,NCE从噪音中采样,文中...